# Exponential equation + geometric progression - examples

1. Crystal
Crystal grows every month 1.9 promile of its mass. For how many months to grow a crystal from weight 360 g to 593 g?
2. Compound interest
Calculate time when deposit in the bank with interest 2.5% p.a. doubles.
3. Demographics
The population grew in the city in 10 years from 42000 to 54500. What is the average annual percentage increase of population?
4. Geometric sequence 3
In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q and n - number of members by their sum s_n.
5. Sequence
Calculate what member of the sequence specified by ? has value 86.
6. Half life
Determine the half life of bismuth, when bismuth weight from the original weight of 32 g was only 2 grams in 242 minutes.
7. To the cinema
Jane at 8 am got message that all 1093 school pupils will go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way the message spread further. At what time all the children in.
8. Geometric sequence
In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
9. Insert into GP
Between numbers 5 and 640 insert as many numbers to form geometric progression so sum of the numbers you entered will be 630. How many numbers you must insert?
10. Geometric progression
In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
11. Microorganisms
The first generation of micro-organisms has a population of 13500 members. Each next generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation.